I am going to write 2 two digit numbers on the board (145 and 152). I want you to build these numbers using your place value blocks .
Now, turn and tell your partner which number is greater. Make sure to use place value vocabulary when you are telling your partner.
As students are discussing, I circulate and ask students questions:
--Why is 152 greater if 145 has more ones than 152?
--How do you know that 152 is greater when they have the same number of hundreds?
After students have talked with their partner for 1-2 minutes, I ask 2-3 students to stand up and share their answers. As students share I make sure to highlight students who are using place value vocabulary to discuss which number is larger. (I.e: a student may respond by saying: I know 152 is greater because even though they have the same number of hundreds, 152 has more tens than 145). I encourage students to use their place value blocks to help explain their answers.
I write a comparison statement on the board.
Turn and Talk: What strategies can we use to compare these two numbers?
I ask three students to share their strategies. As students share their strategies, I write their strategies on the board for future use.
If students are struggling to explain their strategies clearly, I ask them: (1) Is 324 greater than 432 because (pointing to the 4 in the ones place), four is larger than two? (2) Do we only need to look at the hundreds place to compare these numbers? (3) Could we use an addition or subtraction strategy to determine which is greater?
Students need to grasp that, when comparing numbers we start comparing in the hundreds place since hundreds are greatest—students will run into significant trouble if they start comparing in the ones place.
When finished solving and discussing the first problem, I put another problem on the board:
235 ___________ 235
Turn and Talk: What sign should I put here? WHY?
Students need to be able to explain WHY these numbers are equal to one another. They may explain using place value terminology (there are equal number of ones, tens, and hundreds) or they may use another strategy.
In pairs, students work on a Comparing Numbers Game. This is the first time we've played the game, so I model as I explain the game to students.
1) Each student receives a page of numbers. Each student cuts his/her page of numbers to create a "deck" of numbers. (I actually hold up the paper, and cut one or two examples out.)
2) In pairs, each student draws and places one number between the partners, and then they work together to determine which sign would be the correct one to show the comparison between the numbers. [Note: students who are struggling can use cubes or place value blocks to help them.] (I have a student join me, and interactively model this step.)
3) Which ever student has the greatest number, takes both number cards.
4) Students play until they run out of number cards.
As students play the game, I walk around and ask questions:
Why is this number greater? How can you prove your answer?
Can you explain why this number is _________ (equal to, less than, greater than, greatest, lesser)?
Independent practice is tiered based on student understanding of this concept.
Group A: In need of intervention
Students in the A group work with the teacher to compare numbers 100-200. I work with these students to support them in using place value blocks to establish quantities. These are used to compare numbers. My role is to facilitate the process, so that students make meaning of beginning the comparison with the hundreds place, and using that information to decide what needs to be done next. As they make meaning of the quantities, I am also supporting the use of place value vocabulary when explaining their thinking.
Group B: On level
Students in the B group work independently or in partners to compare numbers 200-600. They use place value blocks, if they choose, to help visualize the size of the number. When discussing / explaining their thinking, they will use place value vocabulary.
Group C: Extension
Students in the C group work independently or in partners to compare numbers 200-1200. They are not using place value blocks since students in this group should be able to visualize thousands, hundreds, tens, and ones in their minds. Students in this group also are expected to use place value vocabulary to explain why each number is greater or less.
Today we have worked on comparing numbers. Before we finish our math block, I have one last problem for us to work on together.
Write : 252 ___ 248.
Use your knowledge of place value to tell your partner which number is greater and why.
After 1 minute of sharing ask one or two students to share their answer.
Tomorrow we will continue comparing numbers using our place value knowledge to decide which number is greater!